Geodesic
Some uniform estimates for the transition density of a Brownian motion on a Carnot group and their application to local times
Teoriâ slučajnyh processov, Tome 19 (2014) no. 1, pp. 62-90

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For a specific Brownian motion on a Carnot group several estimates for its transition density are established, which are uniform w.r.t. external parameter. These estimates can be used for studying functionals of any Brownian motion on a Carnot group. As an application we show the existence of the renormalized local time for the increments of Levy area. This result has a lot in common with the well-known existence of the renormalized self-intersection local time for two-dimensional Brownian motion.
Keywords: Brownian motion on Carnot group, local time, Levy area.
Mots-clés : Hormander condition 
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     author = {A. V. Rudenko},
     title = {Some uniform estimates for the transition density of a {Brownian} motion on a {Carnot} group and their application to local times},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {62--90},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2014_19_1_a6/}
}
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A. V. Rudenko. Some uniform estimates for the transition density of a Brownian motion on a Carnot group and their application to local times. Teoriâ slučajnyh processov, Tome 19 (2014) no. 1, pp. 62-90. http://geodesic.mathdoc.fr/item/THSP_2014_19_1_a6/